The present invention relates to a vibration isolating apparatus, and more particularly, to a highly accurate vibration isolating apparatus for blocking vibrations from a floor on which a semiconductor manufacturing apparatus, an electronic microscope or the like is installed, and for controlling a vibrating force from such an apparatus which adversely affects the yield of products and measurement/observation accuracies.
Conventionally, a vibration isolating apparatus of the type mentioned above has relied on a discrete point control method using a set of active actuators for controlling motions of a table. This method, however, has a problem in that control forces of the active actuators interfere with one another to generate unintended vibrations.
While the above problem could be solved by a method that controls each of degrees of motion freedom which are prevented from interfering with one another, this method would require a high performance controller because of complicated calculations needed for the control, resulting in an increased cost.
Considering now an equation of motion about the center of gravity (an inertial system) only taking into account a rigid motion (having a total of six degrees of freedom consisting of two degrees of freedom for translations in the horizontal direction, one degree of freedom for translation in the vertical direction, and three degrees of freedom for rotation about the axes of the translations, which are hereinafter denoted by X, Y, Z, xcex1, xcex2 and xcex3) for a vibration isolating apparatus which has installed on its table a device sensitive to vibrations and is resiliently supported at respective active actuator points, the equation of motion is expressed by the following equation (1):                                                                                           MX                  +                  CX                  +                  KX                                =                F                                                                                        M                =                                  diag                  ⁡                                      [                                          m                      ⁢                                              xe2x80x83                                            ⁢                      m                      ⁢                                              xe2x80x83                                            ⁢                      m                      ⁢                                              xe2x80x83                                            ⁢                                              I                                                  α                          ⁢                                                      xe2x80x83                                                                                              ⁢                                              I                        β                                            ⁢                                              xe2x80x83                                            ⁢                                              I                        γ                                                              ]                                                                                                                                                                                      C                      =                                              [                                                                                                                                                                              ∑                                                                      i                                    =                                    1                                                                    n                                                                ⁢                                                                  xe2x80x83                                                                ⁢                                                                  c                                  xi                                                                                                                                                    0                                                                                      0                                                                                      0                                                                                                                                                        ∑                                                                      i                                    =                                    1                                                                    n                                                                ⁢                                                                  xe2x80x83                                                                ⁢                                                                  (                                                                                                            d                                      zi                                                                        ·                                                                          c                                      xi                                                                                                        )                                                                                                                                                                                    -                                                                                                      ∑                                                                          i                                      =                                      1                                                                        n                                                                    ⁢                                                                      xe2x80x83                                                                    ⁢                                                                      (                                                                                                                  d                                        yi                                                                            ·                                                                              c                                        xi                                                                                                              )                                                                                                                                                                                                                                          0                                                                                                                                                        ∑                                                                      i                                    =                                    1                                                                    n                                                                ⁢                                                                  xe2x80x83                                                                ⁢                                                                  c                                  yi                                                                                                                                                    0                                                                                                                      -                                                                                                      ∑                                                                          i                                      =                                      1                                                                        n                                                                    ⁢                                                                      xe2x80x83                                                                    ⁢                                                                      (                                                                                                                  d                                        zi                                                                            ·                                                                              c                                        yi                                                                                                              )                                                                                                                                                                                      0                                                                                                                                                        ∑                                                                      i                                    =                                    1                                                                    n                                                                ⁢                                                                  xe2x80x83                                                                ⁢                                                                  (                                                                                                            d                                      xi                                                                        ·                                                                          c                                      yi                                                                                                        )                                                                                                                                                                                                        0                                                                                      0                                                                                                                                                        ∑                                                                      i                                    =                                    1                                                                    n                                                                ⁢                                                                  xe2x80x83                                                                ⁢                                                                  c                                  zi                                                                                                                                                                                                                      ∑                                                                      i                                    =                                    1                                                                    n                                                                ⁢                                                                  xe2x80x83                                                                ⁢                                                                  (                                                                                                            d                                      yi                                                                        ·                                                                          c                                      zi                                                                                                        )                                                                                                                                                                                    -                                                                                                      ∑                                                                          i                                      =                                      1                                                                        n                                                                    ⁢                                                                      xe2x80x83                                                                    ⁢                                                                      (                                                                                                                  d                                        xi                                                                            ·                                                                              c                                        zi                                                                                                              )                                                                                                                                                                                      0                                                                                                                                          0                                                                                                                      -                                                                                                      ∑                                                                          i                                      =                                      1                                                                        n                                                                    ⁢                                                                      xe2x80x83                                                                    ⁢                                                                      (                                                                                                                  d                                        zi                                                                            ·                                                                              c                                        yi                                                                                                              )                                                                                                                                                                                                                                                        ∑                                                                      i                                    =                                    1                                                                    n                                                                ⁢                                                                  xe2x80x83                                                                ⁢                                                                  (                                                                                                            d                                      yi                                                                        ·                                                                          c                                      zi                                                                                                        )                                                                                                                                                                                                                      ∑                                                                      i                                    =                                    1                                                                    n                                                                ⁢                                                                  xe2x80x83                                                                ⁢                                                                  (                                                                                                                                                    d                                        zi                                        2                                                                            ·                                                                              c                                        yi                                                                                                              +                                                                                                                  d                                        yi                                        2                                                                            ·                                                                              c                                        zi                                                                                                                                              )                                                                                                                                                                                    -                                                                                                      ∑                                                                          i                                      =                                      1                                                                        n                                                                    ⁢                                                                      xe2x80x83                                                                    ⁢                                                                      (                                                                                                                  d                                        xi                                                                            ·                                                                              d                                        yi                                                                            ·                                                                              c                                        zi                                                                                                              )                                                                                                                                                                                                                      -                                                                                                      ∑                                                                          i                                      =                                      1                                                                        n                                                                    ⁢                                                                      xe2x80x83                                                                    ⁢                                                                      (                                                                                                                  d                                        xi                                                                            ·                                                                              d                                        zi                                                                            ·                                                                              c                                        yi                                                                                                              )                                                                                                                                                                                                                                                                                                            ∑                                                                      i                                    =                                    1                                                                    n                                                                ⁢                                                                  xe2x80x83                                                                ⁢                                                                  (                                                                                                            d                                      zi                                                                        ·                                                                          c                                      xi                                                                                                        )                                                                                                                                                    0                                                                                                                      -                                                                                                      ∑                                                                          i                                      =                                      1                                                                        n                                                                    ⁢                                                                      xe2x80x83                                                                    ⁢                                                                      (                                                                                                                  d                                        xi                                                                            ·                                                                              c                                        zi                                                                                                              )                                                                                                                                                                                                                      -                                                                                                      ∑                                                                          i                                      =                                      1                                                                        n                                                                    ⁢                                                                      xe2x80x83                                                                    ⁢                                                                      (                                                                                                                  d                                        xi                                                                            ·                                                                              d                                        yi                                                                            ·                                                                              c                                        zi                                                                                                              )                                                                                                                                                                                                                                                        ∑                                                                      i                                    =                                    1                                                                    n                                                                ⁢                                                                  xe2x80x83                                                                ⁢                                                                  (                                                                                                                                                    d                                        zi                                        2                                                                            ·                                                                              c                                        xi                                                                                                              +                                                                                                                  d                                        xi                                        2                                                                            ·                                                                              c                                        zi                                                                                                                                              )                                                                                                                                                                                    -                                                                                                      ∑                                                                          i                                      =                                      1                                                                        n                                                                    ⁢                                                                      xe2x80x83                                                                    ⁢                                                                      (                                                                                                                  d                                        yi                                                                            ·                                                                              d                                        zi                                                                            ·                                                                              c                                        xi                                                                                                              )                                                                                                                                                                                                                                                                          -                                                                                                      ∑                                                                          i                                      =                                      1                                                                        n                                                                    ⁢                                                                      xe2x80x83                                                                    ⁢                                                                      (                                                                                                                  d                                        yi                                                                            ·                                                                              c                                        xi                                                                                                              )                                                                                                                                                                                                                                                        ∑                                                                      i                                    =                                    1                                                                    n                                                                ⁢                                                                  xe2x80x83                                                                ⁢                                                                  (                                                                                                            d                                      xi                                                                        ·                                                                          c                                      yi                                                                                                        )                                                                                                                                                    0                                                                                                                      -                                                                                                      ∑                                                                          i                                      =                                      1                                                                        n                                                                    ⁢                                                                      xe2x80x83                                                                    ⁢                                                                      (                                                                                                                  d                                        xi                                                                            ·                                                                              d                                        zi                                                                            ·                                                                              c                                        yi                                                                                                              )                                                                                                                                                                                                                      -                                                                                                      ∑                                                                          i                                      =                                      1                                                                        n                                                                    ⁢                                                                      xe2x80x83                                                                    ⁢                                                                      (                                                                                                                  d                                        yi                                                                            ·                                                                              d                                        zi                                                                            ·                                                                              c                                        xi                                                                                                              )                                                                                                                                                                                                                                                        ∑                                                                      i                                    =                                    1                                                                    n                                                                ⁢                                                                  xe2x80x83                                                                ⁢                                                                  (                                                                                                                                                    d                                        yi                                        2                                                                            ·                                                                              c                                        xi                                                                                                              +                                                                                                                  d                                        xi                                        2                                                                            ·                                                                              c                                        yi                                                                                                                                              )                                                                                                                                                                    ]                                                                                                                                                        K                      =                                              [                                                                                                                                                                              ∑                                                                      i                                    =                                    1                                                                    n                                                                ⁢                                                                  xe2x80x83                                                                ⁢                                                                  k                                  xi                                                                                                                                                    0                                                                                      0                                                                                      0                                                                                                                                                        ∑                                                                      i                                    =                                    1                                                                    n                                                                ⁢                                                                  xe2x80x83                                                                ⁢                                                                  (                                                                                                            d                                      zi                                                                        ·                                                                          k                                      xi                                                                                                        )                                                                                                                                                                                    -                                                                                                      ∑                                                                          i                                      =                                      1                                                                        n                                                                    ⁢                                                                      xe2x80x83                                                                    ⁢                                                                      (                                                                                                                  d                                        yi                                                                            ·                                                                              k                                        xi                                                                                                              )                                                                                                                                                                                                                                          0                                                                                                                                                        ∑                                                                      i                                    =                                    1                                                                    n                                                                ⁢                                                                  xe2x80x83                                                                ⁢                                                                  k                                  yi                                                                                                                                                    0                                                                                                                      -                                                                                                      ∑                                                                          i                                      =                                      1                                                                        n                                                                    ⁢                                                                      xe2x80x83                                                                    ⁢                                                                      (                                                                                                                  d                                        zi                                                                            ·                                                                              k                                        yi                                                                                                              )                                                                                                                                                                                      0                                                                                                                                                        ∑                                                                      i                                    =                                    1                                                                    n                                                                ⁢                                                                  xe2x80x83                                                                ⁢                                                                  (                                                                                                            d                                      xi                                                                        ·                                                                          k                                      yi                                                                                                        )                                                                                                                                                                                                        0                                                                                      0                                                                                                                                                        ∑                                                                      i                                    =                                    1                                                                    n                                                                ⁢                                                                  xe2x80x83                                                                ⁢                                                                  k                                  zi                                                                                                                                                                                                                      ∑                                                                      i                                    =                                    1                                                                    n                                                                ⁢                                                                  xe2x80x83                                                                ⁢                                                                  (                                                                                                            d                                      yi                                                                        ·                                                                          k                                      zi                                                                                                        )                                                                                                                                                                                    -                                                                                                      ∑                                                                          i                                      =                                      1                                                                        n                                                                    ⁢                                                                      xe2x80x83                                                                    ⁢                                                                      (                                                                                                                  d                                        xi                                                                            ·                                                                              k                                        zi                                                                                                              )                                                                                                                                                                                      0                                                                                                                                          0                                                                                                                      -                                                                                                      ∑                                                                          i                                      =                                      1                                                                        n                                                                    ⁢                                                                      xe2x80x83                                                                    ⁢                                                                      (                                                                                                                  d                                        zi                                                                            ·                                                                              k                                        yi                                                                                                              )                                                                                                                                                                                                                                                        ∑                                                                      i                                    =                                    1                                                                    n                                                                ⁢                                                                  xe2x80x83                                                                ⁢                                                                  (                                                                                                            d                                      yi                                                                        ·                                                                          k                                      zi                                                                                                        )                                                                                                                                                                                                                      ∑                                                                      i                                    =                                    1                                                                    n                                                                ⁢                                                                  xe2x80x83                                                                ⁢                                                                  (                                                                                                                                                    d                                        zi                                        2                                                                            ·                                                                              k                                        yi                                                                                                              +                                                                                                                  d                                        yi                                        2                                                                            ·                                                                              k                                        zi                                                                                                                                              )                                                                                                                                                                                    -                                                                                                      ∑                                                                          i                                      =                                      1                                                                        n                                                                    ⁢                                                                      xe2x80x83                                                                    ⁢                                                                      (                                                                                                                  d                                        xi                                                                            ·                                                                              d                                        yi                                                                            ·                                                                              k                                        zi                                                                                                              )                                                                                                                                                                                                                      -                                                                                                      ∑                                                                          i                                      =                                      1                                                                        n                                                                    ⁢                                                                      xe2x80x83                                                                    ⁢                                                                      (                                                                                                                  d                                        xi                                                                            ·                                                                              d                                        zi                                                                            ·                                                                              k                                        yi                                                                                                              )                                                                                                                                                                                                                                                                                                            ∑                                                                      i                                    =                                    1                                                                    n                                                                ⁢                                                                  xe2x80x83                                                                ⁢                                                                  (                                                                                                            d                                      zi                                                                        ·                                                                          k                                      xi                                                                                                        )                                                                                                                                                    0                                                                                                                      -                                                                                                      ∑                                                                          i                                      =                                      1                                                                        n                                                                    ⁢                                                                      xe2x80x83                                                                    ⁢                                                                      (                                                                                                                  d                                        xi                                                                            ·                                                                              k                                        zi                                                                                                              )                                                                                                                                                                                                                      -                                                                                                      ∑                                                                          i                                      =                                      1                                                                        n                                                                    ⁢                                                                      xe2x80x83                                                                    ⁢                                                                      (                                                                                                                  d                                        xi                                                                            ·                                                                              d                                        yi                                                                            ·                                                                              k                                        zi                                                                                                              )                                                                                                                                                                                                                                                        ∑                                                                      i                                    =                                    1                                                                    n                                                                ⁢                                                                  xe2x80x83                                                                ⁢                                                                  (                                                                                                                                                    d                                        zi                                        2                                                                            ·                                                                              k                                        xi                                                                                                              +                                                                                                                  d                                        xi                                        2                                                                            ·                                                                              k                                        zi                                                                                                                                              )                                                                                                                                                                                    -                                                                                                      ∑                                                                          i                                      =                                      1                                                                        n                                                                    ⁢                                                                      xe2x80x83                                                                    ⁢                                                                      (                                                                                                                  d                                        yi                                                                            ·                                                                              d                                        zi                                                                            ·                                                                              k                                        xi                                                                                                              )                                                                                                                                                                                                                                                                          -                                                                                                      ∑                                                                          i                                      =                                      1                                                                        n                                                                    ⁢                                                                      xe2x80x83                                                                    ⁢                                                                      (                                                                                                                  d                                        yi                                                                            ·                                                                              k                                        xi                                                                                                              )                                                                                                                                                                                                                                                        ∑                                                                      i                                    =                                    1                                                                    n                                                                ⁢                                                                  xe2x80x83                                                                ⁢                                                                  (                                                                                                            d                                      xi                                                                        ·                                                                          k                                      yi                                                                                                        )                                                                                                                                                    0                                                                                                                      -                                                                                                      ∑                                                                          i                                      =                                      1                                                                        n                                                                    ⁢                                                                      xe2x80x83                                                                    ⁢                                                                      (                                                                                                                  d                                        xi                                                                            ·                                                                              d                                        zi                                                                            ·                                                                              k                                        yi                                                                                                              )                                                                                                                                                                                                                      -                                                                                                      ∑                                                                          i                                      =                                      1                                                                        n                                                                    ⁢                                                                      xe2x80x83                                                                    ⁢                                                                      (                                                                                                                  d                                        yi                                                                            ·                                                                              d                                        zi                                                                            ·                                                                              k                                        xi                                                                                                              )                                                                                                                                                                                                                                                        ∑                                                                      i                                    =                                    1                                                                    n                                                                ⁢                                                                  xe2x80x83                                                                ⁢                                                                  (                                                                                                                                                    d                                        yi                                        2                                                                            ·                                                                              k                                        xi                                                                                                              +                                                                                                                  d                                        xi                                        2                                                                            ·                                                                              k                                        yi                                                                                                                                              )                                                                                                                                                                    ]                                                                                                                                                        X                      =                                                                                                    [                                                                                                                            x                                                                                                                                                              y                                                                                                                                                              z                                                                                                                                                              α                                                                                                                                                              β                                                                                                                                                              γ                                                                                                                      ]                                                    ⁢                          F                                                =                                                  [                                                                                                                                                      f                                  z                                                                                                                                                                                                                      f                                  y                                                                                                                                                                                                                      f                                  z                                                                                                                                                                                                                      f                                  α                                                                                                                                                                                                                      f                                  β                                                                                                                                                                                                                      f                                  γ                                                                                                                                              ]                                                                                                                                                        }                            (        1        )            
where m represents the overall mass of the table and device; I, moment of inertia about the center of gravity; c, an attenuation coefficient; k, a spring constant; x, y and z, relative displacements of the position of the center of gravity; xcex1, xcex2, xcex3, angular displacements of the center of gravity; d, the coordinate of a position with the center of gravity defined as the origin; and f, a force acting on the center of gravity. Also, suffixes x, y, z, xcex1, xcex2 xcex1xcexdxcex4 xcex3 represent respective degrees of freedom; and i, each resilient supporting point, i.e., an identification number of an active actuator.
The existence of terms other than diagonal components in an attenuation matrix C and a rigid matrix K in the set of equation (1) causes complicated calculations in eliminating the interference.
The present invention has been made in view of the problem mentioned above, and it is an object of the invention to provide a vibration isolating apparatus and a control method therefor which are imposed less restrictions on the positioning of components forming part of the vibration isolating apparatus, such as active actuators, can be implemented by a relatively simple controller (for example, implemented by an analog circuit), and limit the interference of control forces to a practically ignorable degree.
For a vibration isolating apparatus having a common table, points at which the active actuators act their forces exist on substantially the same plane on which the active actuators can be relatively freely positioned. Here, when the active actuators are positioned such that the resilient supporting center thereof matches the Z-axis of the inertial system, the attenuation matrix C and rigid matrix K in the set of equation (1) are expressed as the following equation (2), wherein a vertical translational motion Z is independent of a rotational motion xcex3 about the axis:                                                                                           C                  =                                                            "AutoLeftMatch"                      "AutoRightMatch"                                        [                                          xe2x80x83                                        ⁢                                                                                                                                                      ∑                                                              i                                =                                1                                                            n                                                        ⁢                                                          xe2x80x83                                                        ⁢                                                          c                              xi                                                                                                                                0                                                                          0                                                                          0                                                                                                                                    ∑                                                              i                                =                                1                                                            n                                                        ⁢                                                          xe2x80x83                                                        ⁢                                                          (                                                                                                d                                  zi                                                                ·                                                                  c                                  xi                                                                                            )                                                                                                                                0                                                                                                                      0                                                                                                                                    ∑                                                              i                                =                                1                                                            n                                                        ⁢                                                          xe2x80x83                                                        ⁢                                                          c                              yi                                                                                                                                0                                                                                                      -                                                                                          ∑                                                                  i                                  =                                  1                                                                n                                                            ⁢                                                              xe2x80x83                                                            ⁢                                                              (                                                                                                      d                                    zi                                                                    ·                                                                      c                                    yi                                                                                                  )                                                                                                                                                              0                                                                          0                                                                                                                      0                                                                          0                                                                                                                                    ∑                                                              i                                =                                1                                                            n                                                        ⁢                                                          xe2x80x83                                                        ⁢                                                          c                              zi                                                                                                                                0                                                                          0                                                                          0                                                                                                                      0                                                                                                      -                                                                                          ∑                                                                  i                                  =                                  1                                                                n                                                            ⁢                                                              xe2x80x83                                                            ⁢                                                              (                                                                                                      d                                    zi                                                                    ·                                                                      c                                    yi                                                                                                  )                                                                                                                                                              0                                                                                                                                    ∑                                                              i                                =                                1                                                            n                                                        ⁢                                                          xe2x80x83                                                        ⁢                                                          (                                                                                                                                    d                                    zi                                    2                                                                    ·                                                                      c                                    yi                                                                                                  +                                                                                                      d                                    yi                                    2                                                                    ·                                                                      c                                    zi                                                                                                                              )                                                                                                                                0                                                                          0                                                                                                                                                                                ∑                                                              i                                =                                1                                                            n                                                        ⁢                                                          xe2x80x83                                                        ⁢                                                          (                                                                                                d                                  zi                                                                ·                                                                  c                                  xi                                                                                            )                                                                                                                                0                                                                          0                                                                          0                                                                                                                                    ∑                                                              i                                =                                1                                                            n                                                        ⁢                                                          xe2x80x83                                                        ⁢                                                          (                                                                                                                                    d                                    zi                                    2                                                                    ·                                                                      c                                    xi                                                                                                  +                                                                                                      d                                    xi                                    2                                                                    ·                                                                      c                                    zi                                                                                                                              )                                                                                                                                0                                                                                                                      0                                                                          0                                                                          0                                                                          0                                                                          0                                                                                                                                    ∑                                                              i                                =                                1                                                            n                                                        ⁢                                                          xe2x80x83                                                        ⁢                                                          (                                                                                                                                    d                                    yi                                    2                                                                    ·                                                                      c                                    xi                                                                                                  +                                                                                                      d                                    xi                                    2                                                                    ·                                                                      c                                    yi                                                                                                                              )                                                                                                                                            ⁢                                          xe2x80x83                                        ]                                                                                                                        K                  =                                      "AutoLeftMatch"                                          [                                              xe2x80x83                                            ⁢                                                                                                                                                                  ∑                                                                  i                                  =                                  1                                                                n                                                            ⁢                                                              xe2x80x83                                                            ⁢                                                              k                                xi                                                                                                                                          0                                                                                0                                                                                0                                                                                                                                              ∑                                                                  i                                  =                                  1                                                                n                                                            ⁢                                                              xe2x80x83                                                            ⁢                                                              (                                                                                                      d                                    zi                                                                    ·                                                                      k                                    xi                                                                                                  )                                                                                                                                          0                                                                                                                                0                                                                                                                                              ∑                                                                  i                                  =                                  1                                                                n                                                            ⁢                                                              xe2x80x83                                                            ⁢                                                              k                                yi                                                                                                                                          0                                                                                                              -                                                                                                ∑                                                                      i                                    =                                    1                                                                    n                                                                ⁢                                                                  xe2x80x83                                                                ⁢                                                                  (                                                                                                            d                                      zi                                                                        ·                                                                          k                                      yi                                                                                                        )                                                                                                                                                                          0                                                                                0                                                                                                                                0                                                                                0                                                                                                                                              ∑                                                                  i                                  =                                  1                                                                n                                                            ⁢                                                              xe2x80x83                                                            ⁢                                                              k                                zi                                                                                                                                          0                                                                                0                                                                                0                                                                                                                                0                                                                                                              -                                                                                                ∑                                                                      i                                    =                                    1                                                                    n                                                                ⁢                                                                  xe2x80x83                                                                ⁢                                                                  (                                                                                                            d                                      zi                                                                        ·                                                                          k                                      yi                                                                                                        )                                                                                                                                                                          0                                                                                                                                              ∑                                                                  i                                  =                                  1                                                                n                                                            ⁢                                                              xe2x80x83                                                            ⁢                                                              (                                                                                                                                            d                                      zi                                      2                                                                        ·                                                                          k                                      yi                                                                                                        +                                                                                                            d                                      yi                                      2                                                                        ·                                                                          k                                      zi                                                                                                                                      )                                                                                                                                          0                                                                                0                                                                                                                                                                                              ∑                                                                  i                                  =                                  1                                                                n                                                            ⁢                                                              xe2x80x83                                                            ⁢                                                              (                                                                                                      d                                    zi                                                                    ·                                                                      k                                    xi                                                                                                  )                                                                                                                                          0                                                                                0                                                                                0                                                                                                                                              ∑                                                                  i                                  =                                  1                                                                n                                                            ⁢                                                              xe2x80x83                                                            ⁢                                                              (                                                                                                                                            d                                      zi                                      2                                                                        ·                                                                          k                                      xi                                                                                                        +                                                                                                            d                                      xi                                      2                                                                        ·                                                                          k                                      zi                                                                                                                                      )                                                                                                                                          0                                                                                                                                0                                                                                0                                                                                0                                                                                0                                                                                0                                                                                                                                              ∑                                                                  i                                  =                                  1                                                                n                                                            ⁢                                                              xe2x80x83                                                            ⁢                                                              (                                                                                                                                            d                                      yi                                      2                                                                        ·                                                                          k                                      xi                                                                                                        +                                                                                                            d                                      xi                                      2                                                                        ·                                                                          k                                      yi                                                                                                                                      )                                                                                                                                                        ⁢                                              xe2x80x83                                            ]                                                                                                    }                ⁢                  xe2x80x83                                    (        2        )            
Since it is difficult to exactly know the position of the center of gravity as a practical matter, the resilient supporting center is made coincident with the Z-axis in the inertial system determined by a supposed center of gravity. Since terms caused by errors can be ignored as long as the Z-axis in the interial system substantially matches the Z-axis in the resilient system, the equation (2) can be assumed to be satisfied.
Further, a horizontal translational motion X, a rotational motion xcex2 about the axis of the motion X, a horizontal translational motion Y, and a rotational motion xcex1 about the axis of the motion Y interfere with one and are coupled to one another, as they appear as non- diagonal components of the attenuation matrix C and rigid matrix K shown in the equation (2). However, no problem will arise in practice if such a coupled state can be detected by sensors, a control system is applied in consideration of the coupling of both matrices such that the respective active actuators operate in cooperation. In addition, the coupling as mentioned would not make it difficult to design a control system in consideration of the coupling.
Consequently, according to one aspect of the present invention, there is provided a vibration isolating apparatus for removing a vibration of a table on which a device sensitive to vibrations is mounted, said apparatus comprising:
sensor means for detecting three-dimensional motions of said table;
actuator means for holding said table in a predetermined position; and
a calculating unit for converting three-dimensional detection outputs from said sensor means to activation signals for activating said actuator means on the assumption that the center of resilient support by said actuator means matches the center of gravity, said activation signals being applied to said actuator means.
Said calculating unit comprises:
a first conversion unit for converting detection outputs from said sensor means to a translational motion component representing a translational motion of said table and a rotational motion component representing a rotational motion of said table;
a second conversion unit for converting said translational motion component and said rotational motion component to a force required for removing vibrations of said table; and
a third conversion unit for converting said force to an electric signal for actuating said actuator means.
According to another aspect of the present invention, said sensor means is disposed to detect a translational motion along a first axis vertical to said table, a tranlational motion along a second axis vertical to said first axis and parallel to said table, and a translational motion along a third axis vertical to said second axis and parallel to said table. Said calculating unit is operable to calculate tranlational motion components along said first to third axes and rotational motion components about said first to third axes on the basis of the detection output of said sensor means to produce activation signals from said translational motion components and said rotational motion components for activating said actuating means.
According to a further aspect of the present invention, said actuator means comprises actuators at least one of which is positioned in each of four quadrants partitioned by said second axis and said third axis. Said sensor means comprises at least three first sensors for detecting a translational motion along said first axis, at least two second sensors for detecting a translational motion along said second axis and at least one third sensor for detecting a translational motion along said third axis. Said calculating unit produces said activating signal so as to minimize a difference between forces generated by said actuators.
Said at least two second sensors have different detecting axes each other.
According to a yet further aspect of the present invention, said actuator means comprises:
at least one first actuator disposed on said second axis;
at least one second actuator disposed in either one of two quadrants of four quadrants partitioned by said second axis and said third axis, said two quadrants being opposite to said first actuator with respect to said third axis; and
at least one third actuator disposed in the other of the two quadrants of the four quadrants, said two quadrants being opposite to said first actuator with respect to said third axis.
Said sensor means comprises:
at least three first sensors for detecting a translational motion along said first axis;
at least two second sensors for detecting a translational motion along said second axis; and
at least one third sensor for detecting a translational motion along said third axis.
Said calculating unit produces said activating signal so as to minimize a difference between forces generated by said first to third actuators.
Said at least two second sensors have different detecting axes each other.
According to another aspect of the present invention, there is provided a method of eliminating vibrations from a table on which a device sensitive to vibrations is mounted, comprising the steps of:
providing sensor means for detecting a motion of said table;
providing actuator means for holding said table in a predetermined position;
converting the output of said sensor means to activation signals for activating said actuator means on the assumption that the center of resilient support by said actuator means matches the center of gravity, said activation signals being applied to said actuator means.
As described above, according to the present invention, values measured by the respective sensors are converted to operating amounts of actuators with respect to a total of six degrees of freedom consisting of one degree of freedom each for translation in the vertical direction and for rotation about the axis of the translation of a table resiliently supported by the vibration isolating apparatus, and two degrees of freedom each for translations on the horizontal plane and for rotations about the axes of the translations, on the assumption that the resilient supporting center matches the center of gravity, and based on the two-dimensional positional relationship between the resilient supporting center and the sensors and active actuators. As a result, the vibration isolating apparatus of the present invention can advantageously control each degree of motion freedom with a relatively simple controller such as an analog circuit. Also advantageously, the vibration isolating apparatus can prevent the control forces of the respective actuators from interfering with one another, and provide a high performance vibration isolating apparatus without increasing any cost.
The above and other objects and features of the present invention will be understood more fully from the consideration of the following description taken in connection with the accompanying drawings wherein one example is illustrated by way of example.